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Block #404,837

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2014, 3:43:35 AM Β· Difficulty 10.4309 Β· 6,390,376 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
088796de514500ff71de9dcc5346a4b9c9fdd9194ea70752d7287127361139a7
View on Chainz β†—

Height

#404,837

Difficulty

10.430925

Transactions

1

Size

209 B

Version

2

Bits

0a6e5114

Nonce

3,187,357

Timestamp

2/15/2014, 3:43:35 AM

Confirmations

6,390,376

Mined by

⛏️ P2SHAW6FdqAF2QFTdoj8WBd1FEKDKLmbtgXE2r

Merkle Root

965040086e5bcccbf178349373cbaf9d67f3b96f6646ec3e2f68c1bacdce15ac
Transactions (1)
Coinbase965040086e5bcc…68c1bacdce15ac
1 in β†’ 1 out9.1800 XPM118 B
AW6FdqAF…mbtgXE2r
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.273 Γ— 10⁹⁸(99-digit number)
12732435720518578083…57836047670570422401
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.273 Γ— 10⁹⁸(99-digit number)
12732435720518578083…57836047670570422401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.546 Γ— 10⁹⁸(99-digit number)
25464871441037156167…15672095341140844801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.092 Γ— 10⁹⁸(99-digit number)
50929742882074312335…31344190682281689601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.018 Γ— 10⁹⁹(100-digit number)
10185948576414862467…62688381364563379201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.037 Γ— 10⁹⁹(100-digit number)
20371897152829724934…25376762729126758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.074 Γ— 10⁹⁹(100-digit number)
40743794305659449868…50753525458253516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.148 Γ— 10⁹⁹(100-digit number)
81487588611318899736…01507050916507033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.629 Γ— 10¹⁰⁰(101-digit number)
16297517722263779947…03014101833014067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.259 Γ— 10¹⁰⁰(101-digit number)
32595035444527559894…06028203666028134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.519 Γ— 10¹⁰⁰(101-digit number)
65190070889055119789…12056407332056268801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,605,756 XPMΒ·at block #6,795,212 Β· updates every 60s
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